Spatial velocity

class SpatialVelocity(value=None)[source]

Bases: spatialmath.spatialvector.SpatialM6

Spatial velocity class

Concrete subclass of SpatialM6 that represents the translational and rotational velocity of a rigid-body moving in 3D space.

Inheritance diagram of spatialmath.spatialvector.SpatialVelocity

Seealso: SpatialM6(), SpatialAcceleration()

classmethod Alloc(n=1)

Construct an instance with N default values (BasePoseList superclass method)

Parameters: n (int, optional) – Number of values, defaults to 1
Return type: Self
Returns: pose instance with n default values

X.Alloc(N) creates an instance of the pose class X with N default values, ie. len(X) will be N.

X can be considered a vector of pose objects, and those elements can be referenced X[i] or assigned to X[i] = ....

Note

The default value depends on the pose class and is the result of the empty constructor. For SO2, SE2, SO3, SE3 it is an identity matrix, for a twist class Twist2 or Twist3 it is a zero vector, for a UnitQuaternion or Quaternion it is a zero vector.

Example:

>>> x = X.Alloc(10)
>>> len(x)
10

where X is any of the SMTB classes.

classmethod Empty()

Construct an empty instance (BasePoseList superclass method)

Return type: Self
Returns: pose instance with zero values

Example:

>>> x = X.Empty()
>>> len(x)
0

where X is any of the SMTB classes.

__add__(right)

Overloaded * operator (superclass method)

Returns

sum of spatial vectors

Return type

SpatialVector subclass instance

Raises

TypeError – attempting to add SpatialVectors of different subclass
ValueErrror – attempting to add SpatialVectors with different numbers of values

v1 + v2 is a spatial vector of the same type as v1 and v2 whose value is the element-wise sum of v1 and v2. If both are arrays of spatial vectors V1 (1xN) and V2 (1xN) the result is an array (1xN).

Seealso: __sub__()

__init__(value=None)[source]

Create a new spatial vector (abstract superclass)

Parameters: value – Value of the

SpatialVector(vec) is a spatial vector constructed from the 6-element array-like vec
SpatialVector([V1, V2, ... VN]) is a spatial vector array with N elements, constructed from the 6-element array-like values Vi
SpatialVector(A) is a spatial vector array with N elements, constructed from the columns of the 6xN array A.

__sub__(right)

Overloaded - operator (superclass method)

Returns

difference of spatial vectors

Return type

SpatialVector subclass instance

Raises

TypeError – attempting to subtract SpatialVectors of different subclass
ValueErrror – attempting to subtract SpatialVectors with different numbers of values

v1 - v2 is a spatial vector of the same type as v1 and v2 whose value is the element-wise difference of v1 and v2. If both are arrays of spatial vectors V1 (1xN) and V2 (1xN) the result is an array (1xN).

Seealso: __add__(), __neg__()

append(item)

Append a value to an instance (BasePoseList superclass method)

Parameters: x (Quaternion or UnitQuaternion instance) – the value to append
Raises: ValueError – incorrect type of appended object

Appends the argument to the object’s internal list of values.

Example:

>>> x = X.Alloc(10)
>>> len(x)
10
>>> x.append(X())   # append to the list
>>> len(x)
11

where X is any of the SMTB classes.

Return type: None

clear() → None -- remove all items from S

cross(other)

Spatial vector cross product

Parameters: other (SpatialM6 instance) – spatial motion vector
Returns: cross product of spatial vectors
Return type: SpatialF6 instance if other is SpatialF6 instance
Return type: SpatialM6 instance if other is SpatialM6 instance

v1.cross(v2) is a spatial vector cross product whose result depends on the SpatialVector subclass of v2:

if \(\vec{m} \in \mat{M}^6\) is a spatial motion vector fixed in a body with velocity \(\vec{v}\) then \(\dvec{m} = \vec{v} \times \vec{m}\) or the crm() function.
if \(\vec{f} \in \mat{F}^6\) is a spatial force vector fixed in a body with velocity \(\vec{v}\) then \(\dvec{f} = \vec{v} \times^* \vec{f}\) or the crm() function.

extend(iterable)

Extend sequence of values in an instance (BasePoseList superclass method)

Parameters: x (instance of same type) – the value to extend
Raises: ValueError – incorrect type of appended object

Appends the argument’s values to the object’s internal list of values.

Example:

>>> x = X.Alloc(10)
>>> len(x)
10
>>> x.append(X.Alloc(5))   # extend the list
>>> len(x)
15

where X is any of the SMTB classes.

Return type: None

insert(i, item)

Insert a value to an instance (BasePoseList superclass method)

Parameters

i (int) – element to insert value before
item (instance of same type) – the value to insert

Raises

ValueError – incorrect type of inserted value

Inserts the argument into the object’s internal list of values.

Example:

>>> x = X.Alloc(10)
>>> len(x)
10
>>> x.insert(0, X())   # insert at start of list
>>> len(x)
11
>>> x.insert(10, X())   # append to the list
>>> len(x)
11

where X is any of the SMTB classes.

Note

If i is beyond the end of the list, the item is appended to the list

Return type: None

isvalid(x, check)

Test if vector is valid spatial vector

Parameters

x (numpy.ndarray) – vector to test
check (bool) – ignored

Returns

True if the matrix has shape (6,).

Return type

bool

pop(i=- 1)

Pop value from an instance (BasePoseList superclass method)

Parameters: i (int) – item in the list to pop, default is last
Returns: the popped value
Return type: instance of same type
Raises: IndexError – if there are no values to pop

Removes a value from the value list and returns it. The original instance is modified.

Example:

>>> x = X.Alloc(10)
>>> len(x)
10
>>> y = x.pop()  # pop the last value x[9]
>>> len(x)
9
>>> y = x.pop(0)  # pop the first value x[0]
>>> len(x)
8

where X is any of the SMTB classes.

reverse(): S.reverse() – reverse IN PLACE

property A: Union[List[numpy.ndarray[Any, numpy.dtype[numpy.typing._generic_alias.ScalarType]]], numpy.ndarray[Any, numpy.dtype[numpy.typing._generic_alias.ScalarType]]]

Array value of an instance (BasePoseList superclass method)

Returns: NumPy array value of this instance
Return type: ndarray

X.A is a NumPy array that represents the value of this instance, and has a shape given by X.shape.

Note

This assumes that len(X) == 1, ie. it is a single-valued instance.

property shape

Shape of the object’s interal matrix representation

Returns: (6,)
Return type: tuple